5n^2+2n+6=0

Solution for 5n^2+2n+6=0 equation:

Simplifying
5n2 + 2n + 6 = 0

Reorder the terms:
6 + 2n + 5n2 = 0

Solving
6 + 2n + 5n2 = 0

Solving for variable 'n'.

Begin completing the square.  Divide all terms by
5 the coefficient of the squared term: 

Divide each side by '5'.
1.2 + 0.4n + n2 = 0

Move the constant term to the right:

Add '-1.2' to each side of the equation.
1.2 + 0.4n + -1.2 + n2 = 0 + -1.2

Reorder the terms:
1.2 + -1.2 + 0.4n + n2 = 0 + -1.2

Combine like terms: 1.2 + -1.2 = 0.0
0.0 + 0.4n + n2 = 0 + -1.2
0.4n + n2 = 0 + -1.2

Combine like terms: 0 + -1.2 = -1.2
0.4n + n2 = -1.2

The n term is 0.4n.  Take half its coefficient (0.2).
Square it (0.04) and add it to both sides.

Add '0.04' to each side of the equation.
0.4n + 0.04 + n2 = -1.2 + 0.04

Reorder the terms:
0.04 + 0.4n + n2 = -1.2 + 0.04

Combine like terms: -1.2 + 0.04 = -1.16
0.04 + 0.4n + n2 = -1.16

Factor a perfect square on the left side:
(n + 0.2)(n + 0.2) = -1.16

Can't calculate square root of the right side.

The solution to this equation could not be determined.